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I was looking for the reason as to why a Carnot engine is the most efficient and watched this video on Khan Academy. It used a very clever method of proving this by contradiction.

First, he took the hypothetical better engine and added it to a reversed Carnot engine to show that the new device formed will not obey the second law of thermodynamics.

However, if we instead used the Carnot engine itself instead of the better engine and a very inefficient engine instead of the Carnot, then wouldn't it prove that the Carnot engine is the worse one?

This argument can also be used to prove that no engine is more efficient than another.

Where am I getting it wrong?

I looked at other similar questions but none of it gives the answer.

Vincent Thacker
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Harshit Joshi
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2 Answers2

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Your flaw is in assuming that you can run an arbitrary engine backwards. In order to reverse the operation of a heat engine the heat engine must be reversible, which the Carnot engine is. The proof shows that all reversible engines must have the same efficiency and that no irreversible engine can be more efficient than a reversible one, but does not apply to engines more generally.

By Symmetry
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If an inferior engine is run backwards as a refrigerator by a ideal Carnot engine, the output will be less than 100% of the heat input. There will be no contradiction.

Eric
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